In the absence of external torque for a body revolving about any axis, the quantity that remains constant is

The position vector of a particle is given by $\vec{r} = 2\hat{i} - 6\hat{j} - 12\hat{k}$ units. $A$ force $\vec{F} = p\hat{i} + 3\hat{j} + 6\hat{k}$ units acts on it. For what value of $p$ is the angular momentum conserved?

If the value of torque is zero,then

$A$ thin ring of mass $M$ and radius $R$ is rotating with an angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. If $4$ point masses each of mass $m$ are placed gently at the opposite ends of two mutually perpendicular diameters,what will be the new angular velocity of the system?

$A$ uniform disc of mass $100 \ kg$ and radius $2 \ m$ is rotating at $1 \ rad/s$ about a perpendicular axis passing through its centre. $A$ boy of mass $60 \ kg$ standing at the centre of the disc suddenly jumps to a point which is $1 \ m$ from the centre of the disc. The final angular velocity of the boy (in $rad/s$) is

$A$ horizontal disc rotating freely about a vertical axis through its centre makes $90$ revolutions per minute. $A$ small piece of wax of mass $m$ falls vertically on the disc and sticks to it at a distance $r$ from the axis. If the number of revolutions per minute reduces to $60$,then the moment of inertia of the disc is .........